Robust CUSUM test for time series of counts and its application to analyzing the polio incidence data

Abstract

In this paper, we analyze the polio incidence data based on the Poisson autoregressive models, focusing particularly on change-point detection. Since the data include some strongly deviating observations, we employ the robust cumulative sum (CUSUM) test proposed by Kang and Song (2015) to perform the test for parameter change. Contrary to the result of Kang and Lee (2014), our data analysis indicates that there is no significant change in the case of the CUSUM test with strong robustness and the same result is obtained after ridding the polio data of outliers. We additionally consider the comparison of the forecasting performance. All the results demonstrate that the robust CUSUM test performs adequately in the presence of seemingly outliers.Keywords: Minimum density power divergence estimator, Poisson autoregressive model, robust parameter change test, the polio incidence data.